Carnot Cycles in a Harmonically Confined Ultracold Gas across Bose–Einstein Condensation

Abstract

Carnot cycles of samples of harmonically confined ultracold ${}^{87}$Rb fluids, near and across Bose–Einstein condensation (BEC), are analyzed. This is achieved through the experimental determination of the corresponding equation of state in terms of the appropriate global thermodynamics for non-uniform confined fluids. We focus our attention on the efficiency of the Carnot engine when the cycle occurs for temperatures either above or below the critical temperature and when BEC is crossed during the cycle. The measurement of the cycle efficiency reveals a perfect agreement with the theoretical prediction $(1-T_L/T_H)$, with $T_H$ and $T_L$ serving as the temperatures of the hot and cold heat exchange reservoirs. Other cycles are also considered for comparison.